1. Field of the Invention
The present invention relates to radionuclide spectroscopy analysis using radiation detectors, and, more specifically, to correcting the true coincidence summing and calculating total efficiency during spectroscopy analysis of radionuclides undergoing cascading gamma or X-ray emissions.
2. Description of Related Art Including Information Disclosed Under 37 CFR 1.97 and 1.98
Radioactive decay of a parent nuclide to the ground state of its daughter often results in the emission of several gamma ray photons in a cascade sequence. In some types of decay modes such as Electron Capture (EC) or transitions such as Internal Conversion (IC), X-rays are emitted in conjunction with the cascading gamma rays. During such an event if two photons with different energies are emitted in a cascade, and they are detected within the resolving time of the detector system, the two photons are said to be detected in true coincidence. The detector accumulates the sum total of the energy deposited by these two photons. If a photon deposits its full energy—and would normally be in the photo-peak—then any extra energy deposited from the second photon will remove the initial photon from the photo-peak. As a result, events are lost from the Full Energy Peak (FEP) of the gamma-ray of interest. Such a loss is known as a “summing-out”. Conversely, partial energy depositions from two cascading photons could add up and result in an extra count in the Full Energy Peak (FEP) of a gamma ray of interest. Such a gain in counts is known as “summing-in”. If either of these events occurs, then activity determination based on the normal measurement of the FEP efficiency will be in error, unless a correction is made.
Summing-in leads to an increase of an observable peak area, whereas summing-out leads to a decrease of an observable peak area. The total true coincidence summing effect (COI) with respect to a gamma line of interest (denoted with subscript “A”) of a radionuclide under consideration is:COIA=(1−LAγ−γ−LAγ−X,511)·(1+SAγ−γ)·(1+SAγ−X,511)  Math (1)where LAγ−γ and SAγ−γ are the loss and gain probability due to coincidence between decay gamma-rays, and LAγ−X,511 and SAγ−X,511 are the loss and gain probability due to coincidence between decay gamma-rays and X-rays, and 511 keV annihilation photon. These probabilities are the sum of the partial probabilities calculated for individual decay chains involving the gamma line of interest:
                                          L            A                    =                                    ∑                              i                =                1                            N                        ⁢                          L                              A                ,                i                                                    ,                              S            A                    =                                    ∑                              j                =                1                            M                        ⁢                          S                              A                ,                j                                                                        Math        ⁢                                  ⁢                  (          2          )                    The computation of LAγ−γ and SAγ−γ is well known and described in U.S. Pat. No. 6,225,634; the present invention extends the concept to include coincidence corrections for X-rays and gamma-rays, and the 511 keV photons and gamma-rays, e.g. computation of LAγ−X,511.
It is therefore, necessary to correct the FEP efficiency for true coincidence effects. Various methods have been developed to deal with these “summing-in” and “summing-out” events. However, such methods fall far short of the novel invention disclosed herein.
To compute the summing-in and summing-out probability, L. Moens et al. [J. Radioanal. Nucl. Chem. 70 (1982) 539] suggested the use of gamma-ray intensities and derived the mathematical formulae for practically important cases for gamma-ray true coincidence summing correction. F. De Corte [The k0-Standardization Method: A Move to the Optimization of Reactor Neutron Activation Analysis, Agrégé thesis, Rijksuniversitiet Gent, 1987] updated the approach by Moens, and extended it for the cases of gamma-KX (EC) and gamma-KX(IC) true coincidences, but only for a single decay chain.
V. Kolotov et al. [J. Radioanal. Nucl. Chem. 233 (1998) 95; U.S. Pat. No. 6,225,634] implemented Moen's approach in Canberra Industries, Inc.'s Genie-2000 spectroscopy analysis software product. The implementation is based on the mapping of the efficiencies in the space around the detector. In Kolotov's method, the total sample efficiency is computed by knowing the full energy peak efficiency and the intrinsic Peak-to-Total (P/T) ratio. The method assumes that the introduction of a sample does not affect the P/T ratio for voluminous sources. The true coincidence correction factor at a gamma ray of interest can be obtained by numerical integration of the correction factors for volume elements that are small enough for the efficiencies to be considered constant within them. Furthermore, the software code only corrects for true coincidence summing between decay gamma-rays and not between gamma and X-ray or 511 keV photons as in the present invention.
M. Blaauw [Nucl. Inst. Meth. Phys. Res., A332 (1993) 493] suggested a self-validating calibration method for simultaneous computation of the true coincidence effect and activity in the case of highly efficient point source. Together with S. Gelsema, Blaauw [Nucl. Inst. Meth. Phys. Res., A505 (2003) 311] introduced a third efficiency curve to account for the variation of the detector efficiency over the source volume due to self-attenuation and scattering in the sample. M. Blaauw and Gelsema's method is implemented in Ortec's GammaVision® spectroscopy analysis software product. However, the cascade summing correction results for radionuclides prone to gamma-X ray coincidences is marginal from the published data in the literature [“The evaluation of true coincidence effect on CTBTO-type sample geometry”, The 2003 IEEE Nuclear Science Symposium and Medical Imaging Conference, Portland, Org., Oct. 19-25, 2003].
The GammaVision® product requires a geometry specific source based calibration that is both time consuming and expensive. Further, the performance of GammaVision® for radionuclides prone to gamma-X ray true coincidences summing is marginal, and there is no data available to verify the performance for gamma-511 keV true coincidence effects. Moreover, GammaVision® requires source-based calibrations for true coincidence summing correction, which can be both time consuming and very costly, and the cascade summing correction results are heavily dependent on the radionuclides in the calibration source and source geometry.
Kolotov's method uses a simple intrinsic P/T efficiency ratio calibration to estimate the total efficiency in a volume source. However, this can be used to correct for gamma-gamma true coincidence losses or gains, by utilizing P/T efficiency ratios that are maintained invariant throughout a voluminous source. This approach may introduce a higher uncertainty in the computed true coincidence correction factors. Using this method also requires the use of radioactive sources to determine the P/T efficiency calibration, which is then used to compute the total efficiency.
To date the true coincidence summing correction due to coincidence between gamma and X-rays or gamma and annihilation photons (or 511 keV) has not been adequately considered. Previous cascade summing correction inventions do not rigorously treat the gamma-KX ray and gamma-511 keV true coincidence summing analysis as does the present invention. Alternate methods can be employed using Monte Carlo codes such as MCNP-CP (Berlizov, A. N., MCNP-CP-A Correlated Particle Radiation Source Extension of a General Purpose Monte Carlo N-Particle Transport Code, Applied Modeling and Computations in Nuclear Science. Semkow, T. M., et al., Eds. ACS Symposium Series 945. American Chemical Society, Washington, D.C., 2006, p. 183-194.) and GEANT (Nuclear Instruments & Methods in Physics Research, A 506 (2003) 250-303.). MCNP-CP and GEANT may be used to compute true coincidence summing effects that involve gamma-X rays (and gamma-511 keV photons) true coincidence. However neither MCNP-CP nor GEANT are commonly available and both typically require exceedingly long computational times making such use impractical for other than academic settings.
Accordingly, a need exists for a method for efficiently computing the true coincidence summing correction factors between gamma-KX ray and gamma-511 keV events. Further, a need exists for a method of computing the voxelized total efficiency with gamma-ray buildup correction directly from a mathematical model to improve accuracy of the true coincidence correction factor for voluminous sources. The present invention satisfies these needs and others as demonstrated in the detailed description below.